Abstract:
We apply a promising new method from the field of representations of Lie
groups to calculate integrals over unitary groups, which are important for
multi-antenna communications. To demonstrate the power and simplicity of
this technique, we first re-derive a number of results that have been used
recently in the community of wireless information theory, using only a few
simple steps. In particular, we derive the joint probability distribution of
eigenvalues of the matrix GG , with G a semicorrelated Gaussian random
matrix or a Gaussian random matrix with a non-zero mean. These joint
probability distribution functions can then be used to calculate the moment
generating function of the mutual information for Gaussian MIMO channels
with these probability distribution of their channel matrices G. We then
turn to the previously unsolved problem of calculating the moment generating
function of the mutual information of MIMO channels, which are correlated at
both the receiver and the transmitter. From this moment generating function
we obtain the ergodic average of the mutual information and study the outage
probability. These methods can be applied to a number of other problems. As
a particular example, we examine unitary encoded space-time transmission of
MIMO systems and we derive the received signal distribution when the channel
matrix is correlated at the transmitter end.
Status:
Submitted, March 2004.
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